Explanation Given: Function f ( x ) = x ln x Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Let us assume that p is the critical point of a continuous function f . Moving from left to right If p′ changes from negative to positive at p , then f has local minimum at p If p′ changes from positive to negative at p , then f has local maximum at p Calculation: Function is given as f ( x ) = x ln x The graph of the above function is as follows: From the graph, we see that There is one critical point Also, the function is increasing when x > 1 e Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( x ln x ) Using the product rule of derivative f ′ ( x ) = d d x

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.1, Problem 18P

To determine

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=xlnx

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Chapter 4.1, Problem 17P

Chapter 4.1, Problem 19P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x ln x

Solution Summary: The author explains the function's critical points and the shape of the graph using derivative f(x) = 1e.

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=xlnx

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x ln x

Solution Summary: The author explains the function's critical points and the shape of the graph using derivative f(x) = 1e.

Concept explainers

Videos

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f(x)=xlnx

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=xlnx